A Consistent Implicit Formulation for Nonlinear Finite Element Modeling With Contact and Friction: Part II—Numerical Verification and Results

Using the method derived in Part I, plane-strain sheet-forming processes are analyzed and discussed. Stretch and deep draw forming by cylindrical and flat-bottom punches are presented and compared to closed-form solutions and existing numerical results. The performance of the new algorithm is successfully tested on a complex set of concave, irregular tools by simulating redrawing and reverse drawing with two-sided draw-in and various drawbead forces. The results demonstrate good robustness, accuracy, and efficiency even in the presence of large relative movements between contact surfaces. A quadratic rate of asymptotic convergence is documented for the consistent algorithm and comparison is made to the “linearized” theory which exhibits only linear rate of convergence and reduced numerical stability.